Linear Algebra Problem

Let P be an invertible matrix and assume that A = PMP[itex]^{-1}[/itex]. Where M is

M = [{3,1,0}{0,3,0}{0,0,2}]

Find a matrix B(t) such that e[itex]^{tA}[/itex] = PB(t)P[itex]^{-1}[/itex].

Now this might be an easy problem, but I really have no idea what to do because my lecturer is so bad and the book for the course doesn't cover this material.

I have seen something about A= PBP[itex]^{-1}[/itex] implying e[itex]^{tA}[/itex] = Pe[itex]^{tB}[/itex]P[itex]^{-1}[/itex] so I have tried computing the exponential of M, but to no avail. Any advice is much appreciated.

Let P be an invertible matrix and assume that A = PMP[itex]^{-1}[/itex]. Where M is

M = [{3,1,0}{0,3,0}{0,0,2}]

Find a matrix B(t) such that e[itex]^{tA}[/itex] = PB(t)P[itex]^{-1}[/itex].

Now this might be an easy problem, but I really have no idea what to do because my lecturer is so bad and the book for the course doesn't cover this material.

I have seen something about A= PBP[itex]^{-1}[/itex] implying e[itex]^{tA}[/itex] = Pe[itex]^{tB}[/itex]P[itex]^{-1}[/itex] so I have tried computing the exponential of M, but to no avail. Any advice is much appreciated.

Yes, matrix exponential. This problem is fairly easy because you can split Mt into the sum of a diagonal matrix D and an offdiagonal matrix N which is nilpotent. And they commute with each other. So you can use exp(D+N)=exp(D)exp(N). Finding the exponential of each matrix is pretty easy.